Physical oceanography is the study of physical conditions, processes and variables within the ocean, including temperature-salinity distributions, mixing of the water column, waves, tides, currents and air-sea interaction processes. Here we provide a critical review of how satellite sensors are being used to study physical oceanography processes at the ocean surface and its borders with the atmosphere and sea ice. The paper begins by describing the main sensor types that are used to observe the oceans (visible, thermal infrared and microwave) and the specific observations that each of these sensor types can provide. We then present a critical review of how these sensors and observations are being used to study: (i) ocean surface currents, (ii) storm surges, (iii) sea ice, (iv) atmosphere-ocean gas exchange and (v) surface heat fluxes via phytoplankton. Exciting advances include the use of multiple sensors in synergy to observe temporally varying Arctic sea ice volume, atmosphere-ocean gas fluxes, and the potential for four-dimensional water circulation observations. For each of these applications we explain their relevance to society, review recent advances and capability, and provide a forward look at future prospects and opportunities. We then more generally discuss future opportunities for oceanography-focused remote sensing, which includes the unique European Union Copernicus programme, the potential of the International Space Station and commercial miniature satellites. The increasing availability of global satellite remote-sensing observations means that we are now entering an exciting period for oceanography. The easy access to these high quality data and the continued development of novel platforms is likely to drive further advances in remote sensing of the ocean and atmospheric systems.